econ hw4

HW4 Econ 113

1. The true regression is given by the following equation:

However, you omit X1, X3, and X4 and estimate the following regression instead:

The relationship between the omitted variables and X2 is given by the following equations:

a) Find the estimated values of B0* and B2* in terms of the true B’s. What is the omitted variable bias term for B0*? What is the omitted variable bias term for B2*?

b) Suppose that the true effects of X1, X3, and X4 on Y are given by B1=0.4, B3= -2.4, and B4=3.1. You observe that the relationships between these three variables and X2 are given by ω1=3, γ1=0.5, and ϴ1=0. What is the predicted bias for B2*? Explain your answer as clearly as possible.

4. The average annual income of 100 randomly chosen residents of Santa Cruz is $30,755 with a standard deviation of $20,450.

a) What is the standard deviation of the mean annual income?

b) Test the hypothesis that the average annual income is $32,000 against the alternative that it is less than $32,000 at the 10% level.

c) Test the hypothesis that the average annual income is equal to $33,000 against the alternative that it is not at the 5% level.

d) What is the 95% confidence interval of the average annual income?